A radio communication system using a Multiple Input and Multiple Output (MIMO) scheme has been known. In the MIMO scheme, there are cases in which communication by an eigenmode is performed between a plurality of transmission antennas and a plurality of reception antennas (e.g., see WO 2009/017230 A, JP 2007-512760 W, WO 2008/062587 A, JP 2009-535870 W, JP 2005-510928 W, JP 2008-523665 W, JP 2006-506906 W, and JP 2010-226713 A).
A relation among a radio signal (a transmission signal) x transmitted by a transmission antenna, a radio signal (a reception signal) y received by a reception antenna, and a noise n included in the reception signal y is represented as in Mathematical Formula 1:y=Hx+n  [Mathematical Formula 1]
Here, x represents a vector (transmission signal vector) of Nt×1. Nt represents the number of transmission antennas. n represents a vector (a noise vector) of Nr×1. Nr represents the number of reception antennas. y represents a vector (reception signal vector) of Nr×1. H represents a matrix (a channel matrix) of Nr×Nt. A channel matrix is a matrix having a channel response (channel impulse response) between an i-th reception antenna and a j-th transmission antenna as an element of an i-th row and a j-th column. i represents an integer from 1 to Nr. j represents an integer from 1 to Nt.
A channel matrix H is expressed as a multiplication of three matrices as in Mathematical Formula 2 as a singular value decomposition (SVD) is performed.H=UDVH  [Mathematical Formula 2]
Here, U represents a left singular matrix. V represents a right singular matrix. VH represents a complex conjugate transposed matrix of V. D represents a diagonal matrix as in Mathematical Formula 3.D=diag(√{square root over (λ1)},√{square root over (λ2)}, . . . ,√{square root over (λm)})  [Mathematical Formula 3]
Here, λi represents an eigenvalue of a matrix HHH or a matrix HHH. Here, the number Nt of transmission antennas is assumed to be equal to the number Nr of reception antennas. m represents the number Nt of transmission antennas (or the number Nr of reception antennas). i represents an integer from 1 to m. λi is in proportion to a gain when communication (eigenmode communication) is performed in an eigenmode.
A case in which the transmission signal x acquired by pre-multiplying a pre-process signal s by the right singular matrix V has been transmitted is assumed. The transmission signal x is expressed as in Mathematical Formula 4. In this case, the reception signal y is expressed as in Mathematical Formula 5 derived by substituting Mathematical Formula 4 into Mathematical Formula 1.x=Vs  [Mathematical Formula 4]y=HVs+n  [Mathematical Formula 5]
Further, when a post-process signal z is a signal acquired by pre-multiplying the reception signal y by a complex conjugate transposed matrix UH of the left singular matrix U, the post-process signal z is expressed as in Mathematical Formula 6. Mathematical Formula 6 represents that no interference occurs between channels. In other words, Mathematical Formula 6 represents that communication can be performed in an eigenmode. Here, n′ represents a vector acquired by pre-multiplying a noise vector n by the complex conjugate transposed matrix UH of the left singular matrix U.z=UHy=UHHVs+UHn=Ds+n′  [Mathematical Formula 6]
In a radio communication system, when communication is performed in an eigenmode, a reception side estimates the channel matrix H based on channel state information (CSI). It is possible to estimate the right singular matrix V and the left singular matrix U by performing the singular value decomposition on the estimated channel matrix H. The reception side transfers the estimated right singular matrix V to the transmission side. The transmission side pre-multiplies the pre-process signal s by the right singular matrix V as a transmission weight matrix, and transmits the pre-multiplied signal as the transmission signal x.
The reception side pre-multiplies the received reception signal y by the complex conjugate transposed matrix UH of the left singular matrix U as a reception weight matrix, and acquires the pre-multiplied signal as the post-process signal z. Through the above-described operation, the radio communication system of the MIMO scheme performs communication in the eigenmode, and thus reduces interference between channels and increases a channel capacity.